The present invention relates in general to electrical impedance tomography, and in particular to a new and useful method and apparatus for making electrical impedance images which are significantly faster and more accurate than any previously known method, by first finding the impedance on the boundary of a body to be imaged, using this information to figuratively strip away the outer layer of the body, and thereafter repeating the process in a layer-by-layer manner until information on the full depth of the body is obtained.
An apparatus for practicing electric current computed tomography (ECCT) comprising 32 electrodes and a plurality of current generators is disclosed in U.S. Pat. No. 4,920,490 granted to one of the co-inventors of the present invention. U.S. Pat. No. 4,920,490 is incorporated here by reference and discloses a means for distinguishing one conductivity from another in the body to be imaged.
ECCT is used to determine electrical impedance distribution within a body from electrical measurements made on the surface of the body. It has a wide range of possible applications in medical imaging, geology and mineral exploration, in the nondestructive evaluation of materials, and in the control of manufacturing processes.
There is previous literature on layer-stripping methods for reconstructing internal medium parameters of a body from measurements made on the boundary or outer surface of the body. However, this previous literature generally deals with hyperbolic problems, that problems involving time and wave propagation. These methods are based on the idea of splitting the waves into upward-propagating and downward-propagating components.
In contrast, the process of the present invention deals with an elliptic problem, i.e., a solid-state problem. No wave splitting is involved.
In addition, nearly all the previous literature deals with problems that are essentially one-dimensional, which the medium parameters depend on only one variable
One paper that does deal with a multidimensional elliptic problem is M. Cheney and G. Kristensson, "Three-dimensional inverse scattering: layer-stripping formulae and ill-posedness results," in Inverse Problems 4 (1988) 625-642. This paper considers a time-independent wave equation, which is not the correct mathematical model for the impedance imaging problem.
A second related paper is one that does attempt to solve the multidimensional impedance imaging problem: A. E. Yagle, "A layer stripping fast algorithm for two-dimensional direct current inverse resistivity problem", in IEEE Trans. Geoscience and Remote Sensing GE-25 (1987) 558-563. This paper uses a method that involves analytic continuation, a process that is so unstable that the method described would not work in practice. Moreover, it uses a method that does not work if the medium varies in all dimensions, i.e., for a two-dimensional problem the medium must be only one-dimensional, and for a three-dimensional problem the medium can be only two-dimensional. In contrast, the process of the present invention applies to media that are fully two- or three-dimensional.
Finally, most of the previous work is purely mathematical. In contrast, the present invention is a process that has been reduced to practice.